I got a pretty good condition Trek 400 and it has SunTour Edge components. Unfortunately, the rear Accushift derailleur is missing a cable anchor bolt so I have no way of attaching a cable to it. Are there places where I can buy a replacement part for it or is my best bet to go to my LBS?
Your best bet is to go to your LBS or hardware shop and try a few bolts until you find one that fits.
I don't know if this derailleur came with a special washer to help hold the cable or not, but its not really important that you get an exact match on this part. So long as you find a bolt (and possibly washer) that fits and holds the cable under tension, its fine. If you go to your LBS, they should have something that works (it wouldn't surprise me too much if some random Shimano/SRAM bolt worked; Nathan in the comments notes that its probably M5x0.8).
[In fact, if there was a special washer, you're almost surely not going to find the exact same one aside from buying the same/similar derailleur (e.g. on eBay) and taking it off there, since the parts are over 20 years old. ]
Unless your LBS is a bike museum, I would not expect them to have exactly the right parts, since I'm pretty sure that derailleur is 30 years old.
Looking through http://bikeparts.com I see they have a variety of cable-fixing bolts for current derailleurs, and they're cheap enough you could take a flyer and buy several to see if any fit.
So you might be able to find something that would fit, and that's probably fine. If not, your options are to start trolling eBay, or to have the bolt-anchoring point retapped to fit something that exists today.